Conventional incandescent light bulbs have a wire filament acting as an extended light source with nearly constant intensity throughout its quasi-spherical emission pattern. Here we present a novel family of optical devices that make use of commercially available Lambertian or near-Lambertian LED light sources, in conjunction with tailored optical element bonded to the top surface of the LED. These hybrid devices can emulate the output of traditional incandescent filaments, or can be designed to produce a wide range of light output beam patterns. We call these new devices Virtual Filaments, as they can be designed to appear the same as an incandescent filament, with a similar light output pattern, and having a similar focal position above the base. These new lamps can then be used in the same applications as those they replace, thus eliminating the need to redesign or replace the original luminaire. We present several possible optical designs that can be used with a number of standard LEDs to replace standard incandescent bulbs. In one example we show a design that provides an output with near-uniform intensity across a full beam angle of 300 degrees, from a focal position 20 mm above an LED. Other major advantages of these new devices include their ability to be given sharp cutoffs, to homogenize non-uniform LED light sources and to color-mix the output of RGB LEDs.